Estimation and selection for spatial zero‐inflated count models

Abstract

AbstractThe count data arise in many scientific areas. Our concerns here focus on spatial count responses with an excessive number of zeros and a set of available covariates. Estimating model parameters and selecting important covariates for spatial zero‐inflated count models are both essential. Importantly, to alleviate deviations from model assumptions, we propose a spatial zero‐inflated Poisson‐like methodology to model this type of data, which relies only on assumptions for the first two moments of spatial count responses. We then design an effective iterative estimation procedure between the generalized estimating equation and the weighted least squares method to respectively estimate the regression coefficients and the variogram of the data model. Moreover, the stabilization of estimators is evaluated via a block jackknife technique. Furthermore, a distribution‐free model selection criterion based on an estimate of the mean squared error of the estimated mean structure is proposed to select the best subset of covariates. The effectiveness of the proposed methodology is demonstrated by simulation studies under various scenarios, and a real dataset regarding the number of maternal deaths in Mozambique is analyzed for illustration.